This influence of apparent proportion, a proportion, be it observed, which has no reference to ultimate ends, but which is itself, seemingly, the end and object of operation in many of the forces of nature, is therefore at the root of all our delight in any beautiful form whatsoever. For no form can be beautiful which is not composed of curves whose unity is secured by relations of this kind. Sec. 13. Apparent proportion in melodies of line. Not only however in curvature, but in all associations of lines whatsoever, it is desirable that there should be reciprocal relation, and the eye is unhappy without perception of it. It is utterly vain to endeavor to reduce this proportion to finite rules, for it is as various as musical melody, and the laws to which it is subject are of the same general kind, so that the determination of right or wrong proportion is as much a matter of feeling and experience as the appreciation of good musical composition; not but that there is a science of both, and principles which may not be infringed, but that within these limits the liberty of invention is infinite, and the degrees of excellence infinite also, whence the curious error of Burke in imagining that because he could not fix upon some one given proportion of lines as better than any other, therefore proportion had no value nor influence at all, which is the same as to conclude that there is no such thing as melody in music, because there are melodies more than one. Sec. 14. Error of Burke in this matter. The argument of Burke on this subject is summed up in the following words:--"Examine the head of a beautiful horse, find what proportion that bears to his body and to his limbs, and what relations these have to each other, and when you have settled these proportions, as a standard of beauty, then take a dog or cat, or any other animal, and examine how far the same proportions between their heads and their necks, between those and the body, and so on, are found to hold; I think we may safely say, that they differ in every species, yet that there are individuals found in a great many species, so differing, that have a very striking beauty. Now if it be allowed that very different, and even contrary forms and dispositions, are consistent with beauty, it amounts, I believe, to a concession, that no certain measures operating from a natural principle are necessary to produce it, at least so far as the brute species is concerned."